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For Monday

For Monday. Read chapter 7, sections 1-4 Homework: Chapter 4, exercise 1 Chapter 5, exercise 9. Program 1. Any questions?. Alpha-Beta Pruning. Concept: Avoid looking at subtrees that won’t affect the outcome

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For Monday

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  1. For Monday • Read chapter 7, sections 1-4 • Homework: • Chapter 4, exercise 1 • Chapter 5, exercise 9

  2. Program 1 • Any questions?

  3. Alpha-Beta Pruning • Concept: Avoid looking at subtrees that won’t affect the outcome • Once a subtree is known to be worse than the current best option, don’t consider it further

  4. General Principle • If a node has value n, but the player considering moving to that node has a better choice either at the node’s parent or at some higher node in the tree, that node will never be chosen. • Keep track of MAX’s best choice () and MIN’s best choice () and prune any subtree as soon as it is known to be worse than the current  or  value

  5. function Max-Value (state, game, ,) returns the minimax value of state if Cutoff-Test(state) then return Eval(state) for each s in Successors(state) do  <- Max(, Min-Value(s , game, ,)) if  >=  then return  end return  function Min-Value(state, game, ,) returns the minimax value of state if Cutoff-Test(state) then return Eval(state) for each s in Successors(state) do  <- Min(,Max-Value(s , game, ,)) if  <=  then return  end return 

  6. Effectiveness • Depends on the order in which siblings are considered • Optimal ordering would reduce nodes considered from O(bd) to O(bd/2)--but that requires perfect knowledge • Simple ordering heuristics can help quite a bit

  7. Chance • What if we don’t know what the options are? • Expectiminimax uses the expected value for any node where chance is involved. • Pruning with chance is more difficult. Why?

  8. Determining Expected Values

  9. Imperfect Knowledge • What issues arise when we don’t know everything (as in standard card games)?

  10. State of the Art • Chess – Deep Blue, Hydra, Rybka • Checkers – Chinook (alpha-beta search) • Othello – Logistello • Backgammon – TD-Gammon (learning) • Go • Bridge • Scrabble

  11. Games/Mainstream AI

  12. What about the games we play?

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